LECTURE 10
The open economy
Øystein Børsum
21st March 2006
Overview of forthcoming lectures

Lecture 10: Open economy

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Lecture 11: Open economy and the market for foreign exchange
(Prof. Nymoen)
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The AD-AS framework for the open economy
The market for foreign exchange and the domestic money market
Lecture 12: Fixed and floating exchange rates (Prof. Nymoen)
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Features of a small, open economy with perfect capital mobility
Macroeconomic policy under a fixed and floating exchange rate regimes.
Inflation targeting
Lecture 13: Choice of exchange rate regime

The source of perturbations to the economy and the optimal exchange
rate regime
PART 1
Assumptions and evidence of the
open economy
Overview of assumptions and evidence of the open
economy

Strong growth in exports and international capital flows
motivates modeling the open economy. An economy like
Norway, and most economies indeed, are small and
specialized (engages in trade but cannot influence global
macroeconomic conditions)

There is a market for foreign currency both spot and forward.
Under certain conditions – perfect capital mobility and riskneutral investors – the expected future spot price equals
today’s forward price (uncovered interest rate parity)

In the long run, relative purchasing power parity is a
reasonable condition. This implies real interest rate parity
Strong growth in international trade and capital
flows
World exports, portfolio investments and foreign direct investments, 1970-1996. Bill. 1996-dollars
The forward price for foreign currency
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Spot price of foreign currency
What if you need to buy foreign currency one year from now?
Currency forward contract: Agreement today to buy a specified
amount of foreign currency in one year, where the price is
determined today
By a no arbitrage condition, the forward price is determined by
the spot price of foreign currency and the interest rate
differential between the two currencies
Instead of buying a forward contract, consider the equivalent
strategy of borrowing today in your own currency, buy
currency spot today and invest the foreign currency
Determining the forward price by no arbitrage

Suppose you need 1$ in one year (in period t + 1)

Buy
1
1+if
$ in the spot market today for
Et
1+if
if = foreign rate of interest
Et = Spot exchange rate (price of one unit of foreign currency in terms of the domestic
currency)

Finance your purchase by a one-year loan in your home
currency

When the loan is due, you must pay
Et
(1 + i)
1+if
i = domestic rate of interest

Notice that this strategy is completely risk-free: You know for
sure that you obtain 1 dollar in one year, and how much you
must to pay for it now
Covered and uncovered interest rate parity

Covered interest rate parity (CIP)
Et
Ft ; t+1 = Ẽ+1 =
= (1 + i)
1+if

(1 + i) = (1 + i
f)
Ẽ+1
Et
Ẽt = Forward exchange rate (Ft ; t+1 is an alternative notation)

By log-approximation we can simplify to
i = i f + ẽ+1 - e
ẽt = ln Ẽt

If investors are risk neutral, the forward rate must equal the
expected future exchange rate. This gives uncovered interest
rate parity
i = i f + e e+1 - e
e e+1 = expected future exchange rate (log form)
The evidence on nominal interest rate convergence
in Europe is very convincing
Difference between domestic ten-year government bond yield and the corresponding EU
average, 1994-2000. Percentage points
Source: IMF International Financial Statistics.
International capital mobility and interest rate parity
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Assume that
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Domestic and foreign assets are perfect substitutes
Investors can reallocate their portfolios instantaneously and
costlessly
Investors are risk neutral
Then both covered interest rate parity and uncovered interest
rate parity will hold
The real exchange rate and the international terms
of trade

The real exchange rate is a measure of international
competitiveness

Example: The price of foreign goods measured in kroner relative
to the price of Norwegian goods measured in kroner
f
EP
Er 
P

The international terms of trade
1
P
s of trade  r 
E
EP f
The development of the real exchange rate
depends on inflation differentials and the nominal
exchange rate

Use a log-approximation
f


EP
r
r
f
e  ln E  ln 

e

p
p

 P 
p f  ln P f
p  ln P

Insert the lagged real exchange rate to obtain an expression
for the change in the real exchange rate
er  er1r  re   f   f
(9)
e  e1  e    
(9)
f
f
f
e  e  e1 ,   pf  pf 1 , f  p  p1
e  e  e1 ,   p  p1 ,   p  p1
Relative purchasing power parity

In long-run equilibrium, the real exchange rate must be stable
e e
r
r
1

e    
f
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Relative purchasing power parity (RPPP)
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Reasonable that the purchasing power of a country in the long
run is independent from inflation differentials or changes in the
nominal exchange rate
The evidence on relative purchasing power parity
between Denmark and Germany is convincing
The bilateral exchange rate and the relative price level between Denmark and Germany
Source: Chart 4.1 of Monetary Policy in Denmark, Danmarks Nationalbank, 2003.
Relative purchasing power implies real interest rate
parity in the long run
i  i f  ee1  e
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Uncovered interest rate parity:
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In long-run equilibrium, exchange rate expectations are
correct and we have relative purchasing power parity
ee1  e1  ee1  e  e1  e  e1
e1   1   f1
(RPPP)
i   1  i  
f
f
1

Real interest rate parity
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Conclusion: In the long run, the domestic real interest rate is
tied to the foreign real interest rate. This holds regardless of
the exchange rate regime
Over time, real interest rate differentials tend to
disappear
Long-term real interest rate differential between various countries, 1920-1990. Percentage
points
Source: Centre for European Policy Studies, Adjusting to Leaner Times, 5th Annual Report of the CEPS
Macroeconomic Policy Group, Brussels, July 2003
Key assumptions when modeling the open
economy
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The economy is small

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The economy is specialized
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Global macroeconomic conditions can be taken as given
Domestically produced goods are imperfect substitutes for foreign goods
(relative prices may change)
International capital mobility is perfect and investors are risk neutral

Uncovered interest rate parity holds
Assumptions about the long-run macroeconomic equilibrium:
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Relative purchasing power parity holds
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Real interest rate parity holds